Boolean factor graph model for biological systems: the yeast cell-cycle network

Stephen Kotiang,Ali Eslami

doi:10.1186/s12859-021-04361-8

Abstract

BackgroundThe desire to understand genomic functions and the behavior of complex gene regulatory networks has recently been a major research focus in systems biology. As a result, a plethora of computational and modeling tools have been proposed to identify and infer interactions among biological entities. Here, we consider the general question of the effect of perturbation on the global dynamical network behavior as well as error propagation in biological networks to incite research pertaining to intervention strategies.ResultsThis paper introduces a computational framework that combines the formulation of Boolean networks and factor graphs to explore the global dynamical features of biological systems. A message-passing algorithm is proposed for this formalism to evolve network states as messages in the graph. In addition, the mathematical formulation allows us to describe the dynamics and behavior of error propagation in gene regulatory networks by conducting a density evolution (DE) analysis. The model is applied to assess the network state progression and the impact of gene deletion in the budding yeast cell cycle. Simulation results show that our model predictions match published experimental data. Also, our findings reveal that the sample yeast cell-cycle network is not only robust but also consistent with real high-throughput expression data. Finally, our DE analysis serves as a tool to find the optimal values of network parameters for resilience against perturbations, especially in the inference of genetic graphs.ConclusionOur computational framework provides a useful graphical model and analytical tools to study biological networks. It can be a powerful tool to predict the consequences of gene deletions before conducting wet bench experiments because it proves to be a quick route to predicting biologically relevant dynamic properties without tunable kinetic parameters.

Highlights

The desire to understand genomic functions and the behavior of complex gene regulatory networks has recently been a major research focus in systems biology
We propose a computational framework that combines the formulation of Boolean network (BN) [1] and factor graphs [30, 31] to investigate the global dynamical property and impact of gene knockout in regulatory networks of gene interactions
For BNs of moderate size, i.e., networks with less than 20 nodes such as the illustrative Li model used in this work, our proposed model and methods can allow us to identify the attractors from the initial network states without the need for using a parallelized algorithm to reduce the computation time

Summary

Introduction

The desire to understand genomic functions and the behavior of complex gene regulatory networks has recently been a major research focus in systems biology. The temporal evolution of gene or protein expressions constitutes a dynamical system. Different analytic and computational models have been proposed to capture the behavior of complex gene regulatory networks, including differential equations [2, 3], Bayesian networks [4], and Boolean networks (BNs) [5, 6]. BNs constitute an important class of models for regulatory networks of gene interactions, in that they are simple and capture some fundamental characteristics of gene regulations, and their rule-based structure carries physical and biological meaningful phenomena, for instance, stability, hysteresis, cellular state dynamics, and the possession of a switch-like behavior [8]

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